Synchronization and Power Sharing for Droop-Controlled Inverters in Islanded Microgrids

TL;DR

This paper models droop-controlled inverters in islanded microgrids as a Kuramoto oscillator network, providing stability conditions, power sharing strategies, and a distributed frequency regulation method that works under realistic conditions.

Contribution

It introduces a novel Kuramoto model framework for inverter microgrids, offering stability analysis, power sharing design, and a distributed control algorithm for dynamic load conditions.

Findings

Existence of a unique, stable synchronized solution under certain conditions.

Controller gains can be chosen for optimal power sharing.

Distributed averaging control maintains power sharing while regulating frequency.

Abstract

Motivated by the recent and growing interest in smart grid technology, we study the operation of DC/AC inverters in an inductive microgrid. We show that a network of loads and DC/AC inverters equipped with power-frequency droop controllers can be cast as a Kuramoto model of phase-coupled oscillators. This novel description, together with results from the theory of coupled oscillators, allows us to characterize the behavior of the network of inverters and loads. Specifically, we provide a necessary and sufficient condition for the existence of a synchronized solution that is unique and locally exponentially stable. We present a selection of controller gains leading to a desirable sharing of power among the inverters, and specify the set of loads which can be serviced without violating given actuation constraints. Moreover, we propose a distributed integral controller based on averaging algorithms which dynamically regulates the system frequency in the presence of a time-varying load. Remarkably, this distributed-averaging integral controller has the additional property that it maintains the power sharing properties of the primary droop controller. Our results hold without assumptions on identical line characteristics or voltage magnitudes.